A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations

TL;DR

This paper introduces a novel multivariate spectral hybrid method combining HS and PRP techniques with a derivative-free line search for efficiently solving large-scale nonlinear systems, demonstrating superior performance through numerical experiments.

Contribution

It proposes a new hybrid spectral approach integrating HS and PRP methods with a derivative-free line search, ensuring global convergence for large-scale nonlinear systems.

Findings

Demonstrates good performance compared to existing methods

Proves global convergence of the proposed method

Effective for large-scale nonlinear systems

Abstract

We present a multivariate spectral hybridization of Hestenes-Stiefel (HS) and Polak-Ribiere-Polyak (PRP) method for solving large-scale nonlinear systems of equations. The search direction of the method is obtained by incorporating a multivariate spectral approach with the positive hybridization of Hestenes-Stiefel and Polak-Ribiere-Polyak parameters (HS & PRP hybrid+). By employing a derivative-free nonmonotone line search technique, the global convergence of the sequence generated by the method is proven. Numerical experiments are given to demonstrate the good performance of the method compared with similar methods in the literature designed for solving large-scale nonlinear systems of equations.